Wearable sensors are increasingly taking part in daily activities, not only because of the recent society health concern, but also due to their relevance in the medical industry. In this paper, a galvanic skin response (GSR) extraction technique has been developed in order to interpret electrodermal activity (EDA) records, which can be useful both for ambulatory and health applications. The core of the proposed approach is a novel feature extraction scheme that is based on a nonnegative sparse deconvolution of the observed GSR signals. Unlike previous approaches, the resulting SparsEDA algorithm is fast (immediately extracting the skin conductance level and response), efficient (being able to work with any sampling rate and signal length), and highly interpretable (due to the sparsity of the extracted phasic component of the GSR). Results on real data from 100 different subjects confirm the good performance of the method, which has been released through a free web-based code repository.